A quadratic-equation game
Source: Brazil Math Olympiad, 1998
March 5, 2006
quadraticsalgebraalgebra proposedCombinatorial gamesgame
Problem Statement
Two players play a game as follows. The first player chooses two non-zero integers A and B. The second player forms a quadratic with A, B and 1998 as coefficients (in any order). The first player wins iff the equation has two distinct rational roots. Show that the first player can always win.